A035948 Number of partitions of n into parts not of the form 11k, 11k+5 or 11k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 4 are greater than 1.

1, 1, 2, 3, 5, 6, 9, 12, 17, 22, 30, 38, 51, 64, 83, 104, 133, 164, 207, 254, 316, 386, 475, 576, 704, 848, 1027, 1232, 1483, 1768, 2116, 2512, 2989, 3534, 4184, 4926, 5808, 6812, 7996, 9348, 10932, 12735, 14842, 17238, 20022, 23188, 26850, 31008, 35805

Offset

0,3

Comments

Case k=5,i=5 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ cos(Pi/22) * sqrt(2) * exp(4*Pi*sqrt(n/33)) / (3^(1/4) * 11^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 21 2015

Mathematica

nmax = 60; CoefficientList[Series[Product[1 / ((1 - x^(11*k-1)) * (1 - x^(11*k-2)) * (1 - x^(11*k-3)) * (1 - x^(11*k-4)) * (1 - x^(11*k-7)) * (1 - x^(11*k-8)) * (1 - x^(11*k-9)) * (1 - x^(11*k-10)) ), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 21 2015 *)

Crossrefs

Sequence in context: A225973 A329165 A292444 * A258939 A244747 A241742

Adjacent sequences: A035945 A035946 A035947 * A035949 A035950 A035951

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

a(0)=1 prepended by Seiichi Manyama, May 08 2018

Status

approved